In the given construction $∠ M Y X = 60^{\circ}$ , then $∠ A Y X$ is equal to_________(Assuming that PQ and RS are perpendicular bisectors of AX and AY respectively)

55^{\circ}

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45^{\circ}

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30^{\circ}

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25^{\circ}

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Solution

The correct option is C $30^{\circ}$
During construction, we bisect $∠ M Y X$ and $∠ L X Y$ and these bisectors intersect at a point A.
$\Rightarrow ∠ A Y X = \frac{1}{2} ∠ M Y X$
$\Rightarrow ∠ A Y X = \frac{1}{2} (60^{\circ}) = 30^{\circ}$

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Similar questions

Q. In the given construction

∠ M Y X = 60^{\circ}

, then

∠ A Y X

is equal to_________(Assuming that PQ and RS are perpendicular bisectors of AX and AY respectively)

The steps to construct a triangle with given base angles $∠$ B and $∠$ C and BC + CA + AB, are:.
A. Draw a line segment, say XY equal to BC + CA + AB.
B. Make $∠$ LXY equal to $∠$ B and MYX equal to $∠$ C.
C. Bisect $∠$ LXY and $∠$ MYX. Let these bisectors intersect at a point A.
D. Draw perpendicular bisectors PQ of AX and RS of AY.
E. Let PQ intersect XY at B and RS intersect XY at C. Join AB and AC.

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Given the base angles, say $∠$ B and $∠$ C and BC + CA + AB, construct triangle ABC.

He followed the following steps for the construction.

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2. Make $∠$ LXY equal to $∠$ B and $∠$ MYX equal to $∠$ C.

3. Bisect $∠$ LXY and $∠$ MYX. Let these bisectors intersect at a point A

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5. Let PQ intersect XY at B and RS intersect XY at C. Join AB and AC

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In the given construction ∠MYX=60∘, then ∠AYX is equal to_________(Assuming that PQ and RS are perpendicular bisectors of AX and AY respectively)

The correct option is C 30∘During construction, we bisect ∠MYX and ∠LXY and these bisectors intersect at a point A. ⇒∠AYX=12∠MYX ⇒∠AYX=12(60∘)=30∘

In the given construction $∠ M Y X = 60^{\circ}$ , then $∠ A Y X$ is equal to_________(Assuming that PQ and RS are perpendicular bisectors of AX and AY respectively)

The correct option is C $30^{\circ}$
During construction, we bisect $∠ M Y X$ and $∠ L X Y$ and these bisectors intersect at a point A.
$\Rightarrow ∠ A Y X = \frac{1}{2} ∠ M Y X$
$\Rightarrow ∠ A Y X = \frac{1}{2} (60^{\circ}) = 30^{\circ}$